A stochastic multiple gradient descent algorithm

•A new gradient-based algorithm for stochastic multiobjective optimization problem.•Mean-square and almost-sure convergence of the algorithm proven.•Algorithm tested on a variety of benchmark tests.•Performance compared to two optimization algorithms coupled with a Monte Carlo estimator.•Algorithm c...

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Vydané v:European journal of operational research Ročník 271; číslo 3; s. 808 - 817
Hlavní autori: Mercier, Quentin, Poirion, Fabrice, Désidéri, Jean-Antoine
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 16.12.2018
Elsevier
Predmet:
Engineering Sciences
Materials
Multiobjective stochastic optimization
Multiple gradient descent algorithm Common descent vector
Multiple objective programming
Stochastic gradient algorithm
Stochastic gradient algorithm
Multiobjective stochastic optimization
Multiple gradient descent algorithm Common descent vector
Multiple objective programming
COMMON DESCENT VECTOR
OPTIMISATION MULTIOBJECTIF
MULTIPLE GRADIENT DESCENT ALGORITHM
INCERTITUDE
MULTIOBJECTIVE STOCHASTIC OPTIMIZATION
STOCHASTIC GRADIENT ALGORITHM
MULTIPLE OBJECTIVE PROGRAMMING
ISSN:0377-2217, 1872-6860
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Popis
Shrnutí:•A new gradient-based algorithm for stochastic multiobjective optimization problem.•Mean-square and almost-sure convergence of the algorithm proven.•Algorithm tested on a variety of benchmark tests.•Performance compared to two optimization algorithms coupled with a Monte Carlo estimator.•Algorithm computationally efficient. In this article, we propose a new method for multiobjective optimization problems in which the objective functions are expressed as expectations of random functions. The present method is based on an extension of the classical stochastic gradient algorithm and a deterministic multiobjective algorithm, the Multiple Gradient Descent Algorithm (MGDA). In MGDA a descent direction common to all specified objective functions is identified through a result of convex geometry. The use of this common descent vector and the Pareto stationarity definition into the stochastic gradient algorithm makes the algorithm able to solve multiobjective problems. The mean square and almost sure convergence of this new algorithm are proven considering the classical stochastic gradient algorithm hypothesis. The algorithm efficiency is illustrated on a set of benchmarks with diverse complexity and assessed in comparison with two classical algorithms (NSGA-II, DMS) coupled with a Monte Carlo expectation estimator.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2018.05.064